WARRANTS AND CONVERTIBLES
Answers to Concepts Review and Critical Thinking Questions
When a warrant is issued by the company, and when a warrant is exercised, the number of shares
increases. A call option is a contract between investors and does not affect the number of shares of
If the stock price is less than the exercise price of the warrant at expiration, the warrant is
worthless. Prior to expiration, however, the warrant will have value as long as there is some
probability that the stock price will rise above the exercise price in the time remaining until
expiration. Therefore, if the stock price is below the exercise price of the warrant, the lower
bound on the price of the warrant is zero.
If the stock price is above the exercise price of the warrant, the warrant must be worth at least
the difference between these two prices. If warrants were selling for less than the difference
between the current stock price and the exercise price, an investor could earn an arbitrage profit
(i.e. an immediate cash inflow) by purchasing warrants, exercising them immediately, and
selling the stock.
If the warrant is selling for more than the stock, it would be cheaper to purchase the stock than
to purchase the warrant, which gives its owner the right to buy the stock. Therefore, an upper
bound on the price of any warrant is the firm’s current stock price.
An increase in the stock price volatility increases the bond price. If the stock price becomes more
volatile, the conversion option on the stock becomes more valuable.
The two components of the value of a convertible bond are the straight bond value and the option
value. An increase in interest rates decreases the straight value component of the convertible bond.
Conversely, an increase in interest rates increases the value of the equity call option. Generally, the
effect on the straight bond value will be much greater, so we would expect the bond value to fall,
although not as much as the decrease in a comparable straight bond.
When warrants are exercised, however, the number of shares outstanding increases. This results in
the value of the firm being spread out over a larger number of shares, often leading to a decrease in
value of each individual share. The decrease in the per-share price of a company’s stock due to a
greater number of shares outstanding is known as dilution.
In an efficient capital market the difference between the market value of a convertible bond and the
value of straight bond is the fair price investors pay for the call option that the convertible or the
There are three potential reasons: 1) To match cash flows, that is, they issue securities whose cash
flows match those of the firm. 2) To bypass assessing the risk of the company (risk synergy). For
example, the risk of company start-ups is hard to evaluate. 3) To reduce agency costs associated with
raising money by providing a package that reduces bondholder-stockholder conflicts.